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A planar graph G is said to be triangulated (also called maximal planar) if the addition of any edge to G results in a nonplanar graph. If the special cases of the triangle ...

"The" Sylvester graph is a quintic graph on 36 nodes and 90 edges that is the unique distance-regular graph with intersection array {5,4,2;1,1,4} (Brouwer et al. 1989, ...

A quintic symmetric graph is a quintic graph (i.e., regular of degree 5) that is also symmetric. Since quintic graphs exist only on an even number of nodes, so do symmetric ...

The Schläfli double sixes graph is the Levi graph of the double sixes configuration.

The Harary graph H_(k,n) is a particular example of a k-connected graph with n graph vertices having the smallest possible number of edges. The smallest number of edges ...

The assignment of labels or colors to the edges or vertices of a graph. The most common types of graph colorings are edge coloring and vertex coloring.

In general, a graph product of two graphs G and H is a new graph whose vertex set is V(G)×V(H) and where, for any two vertices (g,h) and (g^',h^') in the product, the ...

An identity graph, sometimes also known as an asymmetric graph or rigid graph (Albertson and Collins 1996), is a graph possessing a single graph automorphism. The numbers of ...

A Laman graph is a graph satisfying Laman's theorem. In other words, it is a graph G have exactly 2n-3 graph edges, where n is the number of graph vertices in G and for which ...

The Pell graph Pi_n is the graph defined as follows. Consider n-tuples of (0,1,2) such that maximal blocks of an odd number of 2's are forbidden. Take these as the vertices ...